Methylmercury

Methylmercury is an esoteric programming language by user:raiseafloppafan7741 in 2026 with some major help from User:PkmnQ and User:Dragoneater67 birthed from some exploration and experimentation with making bases using random combinators. It is actually a combinatory logic language and a near carbon-copy of Lazy K but using the KфΘ basis.

Overview

The combinators used are the Kestrel, the Phoenix, and the Sage bird, each represented in the Unlambda syntax using k, ф (Cyrillic lowercase Ef and not Greek lowercase Phi since fonts disagree on what to make it look like), and Θ respectively.

Table of combinators

Combinator	Bird name	Formula	Expression (CC)	Expression (Unlambda)	Proof
I	Identity bird	Ix = x	ф(KΘ)KK	```ф`kΘkk	ф(KΘ)KKx = KΘ(Kx)(Kx) = Θ(Kx) = Kx(Θ(Kx)) = x Q.E.D.
O	Owl	Oxy = y(xy)	фΘK	``фΘk	фΘKxy = Θ(Ky)(xy) = Ky(Θ(Ky))(xy) = y(xy) Q.E.D.
S	Starling	Sxyz = xz(yz)	ф(ф(KΘ)KK)	`ф```ф`kΘkk	ф(ф(KΘ)KK)xyz = ф(KΘ)KK(xz)(yz) = KΘ(K(xz))(K(xz))(yz) = Θ(K(xz))(yz) = K(xz)(Θ(K(xz)))(yz) = xz(yz) Q.E.D.

I/O model

The I/O model is stolen from Lazy K. The input is a list of Church numerals from 0 to 255 representing the input and the list is terminated by infinite Church numerals for 256. The output is the result of applying the program to the input list, which results in another list of Church numerals from 0 to 255 and terminated by a 256.

Computational class

Fortunately and unfortunately, Methylmercury is Turing-complete as the KфΘ basis can be used to make the Starling, and since SK is Turing-complete then Methylmercury is also Turing-complete. This makes Methylmercury by itself uninteresting, however this begs the question of how far we can take the Phoenix's power.

See also

• PsiK' - another language developed around the same time as the Dimethylmercury experiments
• Lazy K
• Crazy J
• Unlambda
• The Church

External resources

• https://esolanging.wiki/wiki/Draft:Dimethylmercury houses the "experiments". Methylmercury is Candidate 6.